


The Dimensions of Dissent: Doctrinal Heterodoxy in the Linear Liberation Movement

by Cherepashka



Category: Flatland - Edwin A. Abbott
Genre: Academia, Alphabet and Writing, Archival research, Colour Revolt, Future of Flatland, Gen, Gender discrimination in Flatland, Gospel of Three Dimensions, Implied/suggested F/F, Marginalia - Freeform, Movement building, Philosophical Discussions, Poetry, Women in Flatland
Language: English
Status: Completed
Published: 2019-03-22
Updated: 2019-03-22
Packaged: 2019-11-18 08:59:10
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 8
Words: 9,497
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/18117557
Author URL: https://archiveofourown.org/users/Cherepashka/pseuds/Cherepashka
Summary: We received the materials below from a correspondent purporting to be a resident of the world known as Flatland. We await her completed manuscript, but in the meantime we have elected to present her preliminary work here in translation.





	1. Translators' Note

**Author's Note:**

  * For [lirin](https://archiveofourown.org/users/lirin/gifts).



> Hope you enjoy, lirin! I had a lot of fun writing this, so thank you for all the wonderful prompts. I hope I've managed to fill at least some of them to your satisfaction!
> 
> Content warning: Chapter 7 contains characters possibly misgendering a mentioned historical character who, in-universe, was in all likelihood trans or nonbinary as Spacelanders would understand those identities. Mainstream Flatland society, at the relevant time, did not yet recognize nonbinary and non-cis genders.

We received the materials below from a correspondent purporting to be a resident of the world known as Flatland. We have verified both her identity and her authorship of the work she sent us, and we await her completed manuscript, but in the meantime we have elected to present her preliminary work here in translation. We include the author’s introductory letter, her substantive writings, and the archival primary sources she attached, with her own annotations.

The materials herein were originally written in the “lineprint” alphabet of Flatland.1 It was in this form that we first received them, and in this form they might well have remained indecipherable had the author not included, along with her original work, an excerpt in lineprint of the only other known treatise from her world: the memoir readers know as “Flatland: A Romance of Many Dimensions”, composed by a Square and disseminated by his editor and correspondent, the late Edwin A. Abbott. Provided with this facing translation, and familiar as we were with the Square’s memoirs, we were able to decipher the alphabet and translate nearly all of the new material in our possession.

We encountered only one moment of difficulty: certain passages from the original archival material yielded, when translated, what may only be described as gibberish. Further enquiries to our Flatland correspondent revealed that these passages were not merely in lineprint but had been further encrypted via a shift cipher to prevent discovery by unsympathetic readers of what were, at the time, heretical and seditious communications. We have rendered these passages in plaintext, denoting their original encryption with a bracketed annotation: [encrypted].

_________________________________

1 Trs.: According to the author, a native of Flatland, that society uses two main alphabets: “lineprint” and “feelprint”. Lineprint letters are each composed of a short line segment divided into six sub-segments of equal length, which may be darkened or left blank, resulting in sixty-four possible configurations corresponding to sixty-four phonetic characters and punctuation marks. As a sight-based script, lineprint was historically used among those schooled in Sight Recognition; that is, by the gentry and aristocracy of Flatland. The other alphabet, feelprint, consists of a set of acute angles, akin to the ^ (caret) symbol, of whole degree measure and ranging from thirty to sixty degrees. This yields thirty-one characters that can be read by touch, just as a Flatlander might discern or “read” another’s social status by “feeling” that person’s exterior angles. Feelprint was widely considered inferior to lineprint in terms of versatility and aesthetic appeal, but it was by far the more accessible, for its use was widespread among the Equilateral and Isosceles classes and even extended in some eras to Women, despite their lack of access to most formal schooling. 


	2. A Letter to Spaceland

_Autumn Term, Year 2158_

_Esteemed Editor,_

_I am a Straight Line — that is, a Woman — of the world known to you as Flatland. I am called Lemma by my friends, among whose number I presume to count you. I write in hopes that upon perusal of the enclosed materials you will consider publication of my finished dissertation, entitled_ The Dimensions of Dissent: Doctrinal Heterodoxy in the Linear Liberation Movement _, which is currently in progress and for which these materials constitute preparatory research. Alas, my writings will find at best limited circulation among my own people._

_You are no doubt familiar with my world through the memoirs of a noted Square, which were published in your world some years ago, but to my knowledge you have received no communications from Flatland since then. The unfortunate Square’s memoirs primarily depict events that occurred around the beginning of third Millennium; in the two-and-a-half intervening centuries, many momentous changes have roiled the civilization of Flatland. The most significant of these were the spread of the Gospel of Three Dimensions (despite considerable effort on the part of our Circles to prevent it) and the Linear Liberation Movement, which resulted in substantial, albeit incomplete, expansions of the rights of Women. It is the relationship between these two historical developments that is the subject of my planned dissertation._

_I admit that my claims are controversial. To assert, contrary to our Circles’ more politically palatable doctrines, that the Women of the early years of the Movement were literate; that many of them were not only familiar with but subscribed to philosophies that continue to be regarded as rather fringe despite their popularity; and that they were orchestrators rather than mere beneficiaries of a moment of social change — I cannot pretend these are not radical claims. Yet they are where the historical record points, though it seems no one has yet examined parts of that record in detail._

_I had not thought the contentiousness of my arguments a barrier to study until I was informed last month by the Dean of History that I would not be permitted to defend my dissertation or submit it for publication. I appealed the Dean’s injunction first to the Provost and then to the Chancellor of the University, but neither saw fit to overrule the initial decision. I am persuaded that it is my being a Woman that motivated their rulings, as I was offered the option of publishing under my Advisor’s name in lieu of completely changing my dissertation topic. A Woman, perhaps, cannot be trusted to write with academic impartiality on the subject of Linear Liberation; and I am the first and so far only woman to study at the Faculty of History at the University of Wentbridge._

_Unable to bring myself to accept either of the choices offered me, I decided to submit the enclosed abstract, along with an annotated collection of primary sources, to you, in the hopes that they may induce you to accept my finished dissertation for publication once I have completed it. I hope that my research may find an engaged readership and spark further scholarship among a Spaceland audience, happily unconstrained by the societal restrictions in force in my own world. I welcome any feedback you may offer, and I hope that this is only the beginning of a stimulating and productive correspondence._

_Yours most sincerely,_

_Lemma_

_Doctoral Candidate_  
_Faculty of History_  
_University of Wentbridge_  
_Flatland_


	3. Abstract

**The Dimensions of Dissent: Doctrinal Heterodoxy in the Linear Liberation Movement**

Despite the extensive research on the Linear Liberation Movement, relatively little is known about the perspective of those whom the movement most affected: Women. A majority of the literature focuses instead on the process of change among male political elites, who are often credited with being the primary drivers of social change, or on how expansions of the rights and roles available to Women have affected “society at large” — again, implicitly male society. The overall picture of Women themselves that emerges from this body of research depicts them as largely passive beneficiaries of social changes whose origins lay either with Men already occupying positions of power or with broader structural trends. This study challenges that perception, centering the perspectives of Women during the Linear Liberation Movement by closely examining primary sources to which they had access or, crucially, contributed. While the available primary documents created by Women are scant, in part because of their limited access to literacy education relative to Men and in part because many such documents were likely destroyed, the records that survive paint a very different picture than current literature presents. I argue that Women, far from being passive recipients of the benefits of a movement for social change, were in fact that movement’s primary architects; that they were not only versed in relevant political and doctrinal theories of the time but deployed them strategically to advance their movement goals; and, crucially, that the most influential philosophical framework among the Women leading the movement was the Gospel of Three Dimensions. Archival records suggest that it was this belief system, and its growing popularity among both Women and Men of all classes during the early years of the Linear Liberation Movement, that inspired or reinforced many of the ideological tenets and political demands of the movement. This study challenges and complicates existing research on the Linear Liberation Movement, and will hopefully provide the groundwork for new avenues of historical inquiry foregrounding the perspectives of those largely omitted from the narratives so far.


	4. Annotations

**Archival Document #221A-64**

Description: Excerpt from a copy of _Council v. Tetragonos, A Square_ , Case No. 3-CR-2000, Exhibit 14; with handwritten notes  
Date: c. 2000 (original document); c. 2075-2080 (subsequently added handwritten notes)

_[lineprint with handwritten underlining and marginalia]_

> I. "More merciful, more loving!" But these are the qualities of women! And we know that a Circle is a higher Being than a Straight Line, in so far as knowledge and wisdom are more to be esteemed than mere affection.
> 
> Sphere. It is not for me to classify human faculties according to merit. Yet many of the best and wisest in Spaceland think more of the affections than of the understanding, more of your despised Straight Lines than of your belauded Circles.
> 
> ~~Here’s the bit I was telling you about.~~  
>  ~~_Fascinating, agreed. But more than a joke or hallucination?_~~  
>  ~~Can YOU see a Square imagining all this on his own, let alone being daft enough to write it down?~~  
>  ~~_We are._~~  
>  Point. But that is only because my infernal footman is taking an eternity to set out tea!  
>  _Were I less trusting I would suspect him of a deliberate attempt to eavesdrop._  
>  I am less trusting, and do suspect him; my capacity for mercy and love is rapidly diminishing.

* * *

**Lemma’s notes:**

_This fragment of a copy of the well-known memoirs of Tetragonos, the Square who promulgated the Gospel of Three Dimensions, is most notable for the handwritten annotations added some decades later. It is possible to discern two different mouths upon the stylus, and indeed the annotations read as a surreptitious conversation (rather like the notes inattentive students are known to pass amongst each other in a classroom) between the writers, at least one of whom was a Woman; likely both were._

_This fragment establishes that, at the very least, some Women were aware of the Gospel of Three Dimensions, and comprehended it well enough to debate its implications; the underlined portions suggest that they were particularly focused on those parts of Tetragonos’ memoirs that most directly challenged the doctrine of Regularity and the social disparities between Men and Women. It would be venturing into speculation to suggest that the Gospel of Three Dimensions directly inspired the Linear Liberation Movement’s efforts to ideologically deconstruct and dismantle the doctrine of Regularity; but it seems safe to say that the two were in dialogue._

_The identities of the Women are unknown, but as this copy of Tetragonos’ memoirs was found among the records kept by the Circle Callocyclus, a member of the Council who served a few decades after Tetragonos’ death, one or both of the annotators was likely a member of his household. The exchange between the two annotators — the easy debate, and even facetious banter, between them — suggests a dialogue between social equals: perhaps Callocyclus’ wife or daughter and a close friend or cousin. Callocyclus’ wife Arcana and his daughter Synchordia are likely to have been deeply involved in the Linear Liberation Movement and, I posit, were among its leaders; they were in attendance at most of the Council proceedings eventually resulting in policy change, and Synchordia was briefly arrested at a demonstration during the peak years of the Movement; Callocyclus himself, though initially opposed to expanding rights for Women, eventually became one of the Movement’s staunchest supporters on the Council, perhaps at the urging of his female family members._

_A significant portion of the annotations have been stricken through, apparently some time after the marginal notes were first added; these portions were somewhat difficult to read, but new techniques of breaking light into a spectrum and creating images of layered print exposed in various light spectra have facilitated the discernment of the underlying layers. It is unclear why the annotators, or some later annotator, attempted to strike out or conceal parts of the written dialogue, but given their focus on the most heterodox and politically subversive portions of the text, this may have been an attempt to destroy evidence of discussions that would have been seen as seditious._

* * *

Arcana is reading when Lateralis comes to call on her, but she swiftly tucks the text away as soon as the maid shows Lateralis through the Women’s door. It is an open secret that the wives and daughters of Polygons and Circles are usually literate, for households as large and complicated as theirs are difficult enough to manage without the added hindrance of not being able to note anything down. But it wouldn’t do to flaunt that fact before the maid, so Lateralis waits demurely, quite still except for the gentle undulation of her back, until the greetings are done and the young Woman has departed. Only then does she ask, “Whatever were you reading, my dear? It looked most diverting, and I am sorry if I have interrupted you.”

“Oh!” Arcana’s smiles, Lateralis thinks, always seem just the slightest bit wicked. “You haven’t interrupted me at all; in fact, I was glad when you said you would call today, for I would welcome your thoughts on this very matter.” Lateralis warms, pleased and gratified. Arcana always seems so quick with her opinions, yet here she is seeking Lateralis’. “You know, I presume, of the recent controversies surrounding a philosophy called the Gospel of Three Dimensions?”

Lateralis does; she spent all of breakfast this morning listening to her father Isoradian, whom most regard as a venerable Priest but who at mealtimes tends to wax spectacularly dull, complain about an outbreak of dangerous doctrines among certain of the lower classes. ‘Outbreak’ is his word; he speaks of such things as though they are diseases, infectious and deadly, which must be quarantined and eradicated. Lateralis thinks this particular outbreak smacks more of comedy than contagion; the thought of there being _three_ dimensions, after all, is so absurd as to be laughable. “I was under the impression that it was not so much a proper _philosophy_ as a rather widespread delusion.”

“So was I, at first. But rumour and conjecture do tend to make such a hash of things, and now that I have seen at the original writings on the subject, I am not so sure.”

“The original— Arcana, you don’t mean to say you’ve—”

“Indeed I have!” Arcana cries. Lateralis shushes her and stifles the urge check the hallways for eavesdropping house staff; literate Women might be tolerated, provided the Women are of a certain class, but Women who pilfer confiscated Council records certainly will not be if it is found out. Arcana lowers her voice but continues undaunted. “You know it was all started by that poor Square, at the very beginning of the century. Everyone thought him quite mad.”

“I suppose even respectable Squares are not immune to occasional fits of insanity.” Men’s minds, after all, are susceptible to all sorts of folly, which, between Lateralis’ father and Arcana’s husband, they both know well — though neither would say so aloud before those Men. Even so, Lateralis has to concede that the rumours she has heard of this Gospel of Three Dimensions seem well outside the bounds of normal male eccentricity.

“But he never recanted, even after decades in prison. In fact, he kept writing all his life about this supposed Third Dimension. When he finally died, the Council went through his effects to confiscate anything that might be, well, dangerous, before returning the rest to his family.” One corner of her mouth tilts up. “And it happens that Callocyclus was just appointed Keeper of Records for the Council.”

Well, that explains how Callocyclus got hold of these heretical memoirs, but Arcana’s Councilman husband has always struck Lateralis as prim and stodgy next to his much livelier wife, and very concerned with the propriety of Council business. He is also, however, a bit absent-minded. Lateralis fixes her friend with a shrewd glance. “This doesn’t seem the sort of thing Callocyclus would delegate to you.”

“Well, no,” Arcana admits, and now her smile is positively conspiratorial, “but he did delegate to me the task of tidying his study a bit. What am I to do if he leaves confiscated documents in a stack right on the northside of his desk? I can’t know where to put them if I do not stop to find out what they are.”

Lateralis cannot hold back a startled laugh. Her friend’s temerity often shocks her, but it is also half the reason she enjoys Arcana’s company so much. The unpredictability of it — she never knows what adventures, or misadventures, Arcana will lead her into — sets off a delicious flutter in her stomach.

“Have no fear, the Council made a number of copies; he won't notice one missing. Lateralis, even if they are delusions, they’re such fascinating ones! This Square says there is such a direction as _up_ , which is different from _north_ though I cannot say how, from which one can see the insides of everything! And he claims to have encountered some sort of being called a ‘Sphere’, which is an infinite number of Circles somehow stuck together.”

“Gracious!” She fights down laughter at the idea of so many dignified Circles squashed together, like the soap bubbles in her bath, jostling and crowding and _feeling_ one another. How mortifying! When she envisions her own father Isoradian caught up in the crush, the laughter spills out. Arcana chuckles too, but her eye is thoughtful.

“I know it sounds silly, but the ideas come across as much more coherent than the ravings of a madman. I am struggling to explain it; you must read it for yourself. There are some particularly interesting passages on the subject of Men and Women and the sources of moral worth.”

“Oh?”

“This ‘Sphere’ person seems to suggest that we ought to be less concerned with Regularity than with other qualities. Not dissimilar to the ideas promulgated by the Chromatic Seditionists.”

And not dissimilar, Lateralis realizes, to some of the ideas she has heard from Arcana’s own lips, though always in such a tone as to leave open the possibility that she speaks entirely in jest. ‘If the Council were half as skilled at managing each other as we are at managing them, they could get through the business of governing in a quarter of the time,’ she had muttered to Lateralis once, in the midst of Callocyclus’ laments that two of his fellow Councilmembers were utterly ill-suited to their positions, oblivious to the fact that they were perfectly suited to — not to mention covetous of — each other’s. It was Arcana who invited one home for luncheon and the other for supper, and mourned to each that the other seemed horribly unhappy with his work and needed rescue, if only she could see a way to accomplish it without wounding his pride. By the time the meals were over, each Councilman was convinced it would be a wonderfully noble and self-sacrificing thing to suggest an exchange of positions on pretence of his own unhappiness with his current role, and supper the following day saw Callocyclus remarking with surprise on an unexpected reallocation of Council duties. ‘The more Circles that are in a room together,’ Arcana had whispered, ‘the blinder they seem to be to simple solutions.’

“But do you think there is any _truth_ to it?” Lateralis asks now, doubtfully.

Arcana frowns. “It does seem terribly farfetched. But, you know, I think this may not be the first time we have had a supposed visitation from the Third Dimension. I overheard Callocyclus talking with the Chief Circle’s Secretary about it, and he said something about reports of a similar apparition at the beginning of the first Millennium, and again at the second. Does it not seem equally if not more implausible that three unrelated people who don’t know anything of each other would have exactly the same delusion, exactly a Millennium apart? I have been struggling over what to make of it for days. But I’ve got most of the writings here now—” she pulls the sheaf of papers from where she had hastily hidden it behind a potted plant— “and you must look at it at leisure and tell me what _you_ think.”

Once again Lateralis finds herself flushing with pleasure. She wishes she had Arcana’s gift for making her friends feel as if they are taken into the most delicious of confidences, trusted and worthy and permitted to join a select inner circle. Lateralis suspects that Callocyclus’ seat on the Council is due in no small part to his wife’s skill at inspiring such camaraderie; certainly there seems little enough in Callocyclus himself that would recommend him to the position.

They are passing the journal back and forth, deep in discussion about the mysterious property the Square calls _omnividence_ , when the clatter of dishes interrupts them. Startled, they both fall silent as the footman edges through the door with a tray of tea things, and then share a vexed glance as he begins to set them out. They cannot continue their conversation before a witness! Then all at once, Arcana grins, stretches past Lateralis, and nudges something toward her. Lateralis grins too when she sees what it is: a stylus.


	5. Correspondence

**Archival Documents #435G-39 to -42**

Description: Letters between the Priest Isoradian and the Hexagon Tessellatus  
Date: Spring 2082

_[handwritten lineprint] ___

> Dear Sir,
> 
> I beg you will excuse my contacting you without prior introduction, and with a rather unusual request. I do so on behalf of my dear daughter Lateralis, who has in recent months taken a charitable interest in the plight of Widows, and who has heard through a mutual acquaintance that your mother was herself recently widowed. 
> 
> My daughter has taken to hosting small afternoon gatherings, generally devoted to card parties, music, and other gentle pursuits, to which she has invited a number of Widows of respectable character. She is particularly anxious to extend an invitation to your mother, having learned that your mother’s father regrettably spent most of the latter half of his life incarcerated; which unfortunate circumstance, I hasten to add, I do not see as in any way impugning your own character, for by all accounts you have never demonstrated less than the highest moral sensibilities. Yet the fact remains that, while you no doubt provide more than adequately for your mother’s maintenance, she cannot have escaped being disadvantaged by the absence of a paternal figure in her earlier years of Womanhood.
> 
> My daughter, being easily moved to pity and compassion, was most distressed upon learning of your mother’s circumstances, and would not rest until I had promised to write you. She is hosting another of her gatherings three days from now at our residence, and graciously begs you to convey an invitation to your mother. Please send your reply to G—— Hall, and we very much hope to make your and your mother’s acquaintance in person three days hence.
> 
> Again, I beg your indulgence for my presumption in writing to you so suddenly and familiarly despite our having no prior connection; if you are a father of daughters, you will understand that they elicit even greater indulgences from their parents.
> 
> Yours sincerely,  
>  Isoradian, a Circle
> 
> ——————
> 
> Esteemed Priest Isoradian,
> 
> You need ask no indulgence for your letter of yesterday; indeed it is my great honour that one of your stature should so condescend to take notice of my humble self and my family.
> 
> My mother, too, is greatly honoured, and very much wishes she could accept your most daughter’s most generous invitation. But alas, being quite elderly and, of late, infirm, she finds it very difficult to travel outside the home, and I fear even the short distance to and from your residence would prove too physically taxing. 
> 
> I must therefore convey her deepest regrets, and add to them my own, that we must decline your daughter’s invitation, though we greatly appreciate the kindness that prompted it. I hope you will understand that my mother and I intend no offense; indeed, it is my hope that her health will soon improve, and that, should your daughter see fit to extend a similar invitation some months from now, my mother will be able to accept.
> 
> With utmost gratitude,  
>  Tessellatus, a Hexagon
> 
> ——————
> 
> Dear Sir,
> 
> My daughter and I of course take no offense, and we both, she especially, are greatly saddened to hear of your mother’s ill health. In fact, my daughter was so distressed at the prospect that your mother would miss her next gathering, that she prevailed upon me to suggest an alternative: that she come to see your mother at your residence instead. 
> 
> I must say that I counseled her against the temerity of, in effect, inviting herself as a guest into your home, and apologize for any presumption on her part and by extension mine in suggesting it. But once Lateralis learned that your mother is unable to travel to G—— Hall, nothing would do but that I proposed this option instead. If you are inclined to accept, might she call on you Thursday next, after luncheon?
> 
> Yours sincerely,  
>  Isoradian, a Circle 
> 
> ——————
> 
> Esteemed Priest Isoradian,
> 
> Truly, your generosity, and your daughter’s kindness, know no bounds. There is no need to go so far out of your way to accommodate my mother, but if your daughter insists, then she would be delighted to see her Thursday next.
> 
> With highest regards,  
>  Tessellatus, a Hexagon

* * *

**Lemma’s notes:**

_At first glance this correspondence, which unlike the rest of the materials I examined was neither produced nor amended by Women, might appear unconnected to the question of the ideological underpinnings of the Linear Liberation Movement. However, its relevance becomes clear upon consideration of the identity of Isoradian’s correspondent: the Hexagon Tessellatus was the grandson of Tetragonos, the Square incarcerated for attempting to preach the Gospel of Three Dimensions; Tessellatus’ mother, the subject of these letters, was Tetragonos’ daughter._

_If the marked insistence of Isoradian’s daughter, Lateralis, on meeting in person with Tetragonos’ daughter seems misplaced, and her purported charitable interest a thin disguise for some ulterior motive, I posit that that motive was in fact an interest in Tetragonos’ works. Later writings by Lateralis which I have discovered indicate that she was keenly interested in hypothesizing the mathematics of a three-dimensional world, and she may have wished to obtain from Tetragonos’ daughter a more complete and accurate account of her father’s experiences and teachings. Crucially, Lateralis too was almost certainly a ringleader among the early Linear Liberation organisers, at least if her father’s repeated complaints, recorded in Council minutes, about his daughter’s exhortations to change the policies governing Women are any indication._

_At any rate these letters establish that Lateralis almost certainly met in person with Tetragonos' daughter. In other words, they establish that a Woman both close to the highest Circles of power and involved in orchestrating the Linear Liberation Movement took an unusually strong and apparently unwarranted interest in the family of the Square behind the Gospel of Three Dimensions; an interest that makes sense if it was in fact the Gospel that drew her attention._

* * *

In the end, Lateralis brings Arcana and Diatomis with her when she goes to see Perigramma. Arcana, of course, has been bursting with curiosity to meet the famous Square’s daughter, who by now is positively ancient, ever since Lateralis contrived a pretense to contact her. She asks Diatomis as the third because, of the small cohort of Women now meeting and corresponding regularly about Women’s advancement, Diatomis tends to have the most astute perspectives on how the problems faced by Women are bound up in other issues: the doctrine of Regularity, the polygonist class system, the subjugation of those deemed mentally ill — such as Tetragonos the Square. Lateralis is a bit worried that three of them together will be rather overwhelming for the older Woman, but in the end her desire to have others’ perspectives on whatever Perigramma might say wins out, and she merely cautions the others to proceed gently. 

When they arrive, she realizes she needn’t have worried. Perigramma can hardly walk, and her eye is dim with age, but her hearing is as sharp as anyone’s; her mind, if anything, sharper. She seems pleased enough to have company, but unlike her son, she at once sees through Lateralis’ sudden solicitousness toward Widows, and the younger Women find themselves revealing within minutes the real impetus for their visit. 

“Well, of course, the official story is that my father was a lunatic,” she tells them frankly, when they broach the subject. “My mother certainly thought so, anyhow. She found the whole incident terribly distressing.”

“She must have,” Arcana says sympathetically. “But… you don’t think the official story is correct?”

“My dear, it’s got about as many holes as a honeycomb. But then, so did the load of claptrap Father tried to give us when he returned; and my vision might be going now but it was sharp as my ends back then, and I can neither forget nor deny what I saw. Haven’t spoken of it in years, of course. No one would believe me if I did.”

Lateralis exchanges glances with Diatomis and Arcana. “We would.”

Perigramma smiles. “Would you now? I was rather tempted for quite a while to disbelieve it myself. In many ways that seemed the easier route.”

“If we were inclined to believe things only because they were easy, we wouldn’t be here,” Diatomis says firmly. 

Still, now that the prospect of actually relating what happened all those years ago, to an audience who will not dismiss her, is at hand, Perigramma hesitates. “Would you believe me,” she says at last, slowly, “if I told you my father disappeared — quite literally disappeared, and then reappeared hours later, as if by magic?”

“You mean…”

“I don’t think he knew I was watching, but I saw it happen. When he returned, that is. One moment the front hallway was empty, and the next, all of a sudden, there he was.”

“Perhaps he simply, I don’t know, slipped in from an adjoining room or through the door while you glanced away?”

“I told you you’d find it hard to believe. But no, the doors were all closed, except the one to my room. I tell you he wasn’t there, and then he was. And then, a moment later there was someone else with him.”

The three younger Women exchange another glance. “A Circle?” Lateralis guesses. It would confirm the account in Tetragonos’ memoirs.

Again, Perigramma hesitates. “Yes, but not like any Circle I’ve ever seen. You can tell, usually, you know, that there’s just a hint of graininess to the perimeters of even the highest Circles. Of course, they’re all really Polygons, only with very many, very small sides. My Sight Recognition was always quite good, and I could generally always tell. But with this one, I couldn’t. His perimeter really did look completely smooth. My dears, I cannot pretend I ever delved half as deeply as my father did into the nature of infinitesimals, for after all he was a Mathematician and I am not. But I can tell you that that Circle was composed of true infinitesimals if ever anyone was.”

“And did you learn anything of who he was? Or where he might have come from? He wasn’t anyone on the Council, was he?”

Perigramma chuckled. “Hardly. He didn’t even sound like he was quite, you know, of this world. His voice rather echoed, as if it were coming from multiple directions at once. It was positively eerie, now that I look back, but of course as a younger Woman then I only found it exciting.”

This comported all too well with the impression of the mysterious Sphere Lateralis had gotten from Tetragonos’ writings. 

“Might I ask something?” she said, thoughtful. “About what size was he?”

Perigramma looked startled. “Why, that was the oddest thing! He wasn’t any one size. At first he seemed quite small, smaller even than a child, and then as he and Father were speaking he swelled to a bit larger than most Circles I’ve seen — and then as he departed… Well. He didn’t use the door, I can tell you that. He simply shrunk again, until he was quite tiny, and then shrunk even more until he was nothing but a point, and I might have been looking at a Woman straight on — and then he vanished! Just as father had, though I’ve no idea where to.”

“What did your father say about all this?” Diatomis asks.

“He gave my mother some rigmarole about having had urgent business at the request of a Councilmember, and I suspect she accepted it because the alternatives were either that he was mad or that something occult was at work. But I know he hadn’t done anything to attract the notice of the Council up to then. That all came later — _after_ this business with the shrinking Circle, and because of it. And they certainly weren’t engaging him for business.”

Arcana meets Lateralis’ eyes in silent conference, and Lateralis reads the question there easily enough. _Should we tell her?_ Diatomis is already nodding, but Lateralis can see that Arcana isn’t so sure. Would the knowledge help, or simply make things harder now for a daughter who lost her father decades ago?

“Of course, they told us that he _was_ mad, afterwards,” Perigramma says, now sounding wistful, and rather sad. “Perhaps he was; but I know what I saw, and none of the official stories could account for it.”

That decides them. “We do not know if your father was of sound mind,” Arcana says gently. “But we have read his writings on the matter, and they are at least internally coherent, if rather fantastical.”

Perigramma gasps. “But those were all confiscated!”

“Indeed they were. But we may have… happened upon a copy or two, in the course of our own studies.”

The corner of Perigramma’s mouth quirks up. “How serendipitous.”

Lateralis clears her throat. “Indeed. Your father claims, in short, to have been granted sight of a third dimension.”

“A third dimension? But how can that be?”

“We do not know; we are still attempting to puzzle it out ourselves. But if you like, we can perhaps bring you a copy of your father’s writings. In strictest confidence, of course. I can’t say if they will answer your questions, but they may at least fill in some of the holes.”

“You would do that?” Perigramma breathes. “But — oh, I cannot read lineprint anymore.”

“I’ll copy it out in feelprint, then,” Diatomis interjects. 

“Thank you, my dears.” Perigramma’s voice is quiet, but Lateralis feels the force behind her words.

“No,” she says. “Thank _you_.”


	6. Doggerel

**Archival Document #541E-07**

Description: Broadside, partially torn, of a popular vulgar poem  
Date: c. 2090

_[lineprint]_

> But when at last she pierced the Priest,  
>  No priestly flesh she found,  
>  No giblets, guts, or viscera  
>  Within the Stately Round.  
>  Instead: A second highborn Beast!—  
>  Consumed without a trace—  
>  Who sought to seize a kiss or a  
>  Libidinous embrace  
>  From she who penetrated deep  
>  Beneath her husband’s skin—  
>  She halted not, but stabbed him fain,  
>  This Priest who lay within.  
>  But even then no blood did seep,  
>  For past the bound’ry lay,  
>  Within the pair so newly slain,  
>  Yet one more Priest to slay!  
>  But did she balk? And did she blench?  
>  Not she! Her will was strong!  
>  Dauntless, she said, this doughty wench:  
>  “ ’Tis well I am so long!”  
> 
> 
> _[handwritten feelprint, encrypted]_
> 
> Diatomis, you fiend, I cannot believe you actually got this published!  
>  _Anonymously, of course. Favilla delivered it for me._  
>  That is no defense; it only demonstrates you select employees as fiendish as yourself!  
>  _A dire insult! I seem to recall you laughing uproariously at it when we read it aloud after last month’s meeting._  
>  That was in private!  
>  _Well, now everyone gets to share the fun!_

* * *

**Lemma’s notes:**

_This is the final stanza of a poem that presented a darkly comedic take on the climactic incident during the final days of the Colour Revolt in which twenty-three Circles were abruptly and violently murdered by their wives. It circulated in the late twenty-first century, both among the Isosceles and Equilateral classes, as has been documented, and — perhaps more surprisingly — among social elites. It was widely regarded as in poor taste, yet was also wildly popular._

_This copy is notable because, to my knowledge, it is the only one that presents a hint to the anonymous author’s identity, in the ciphered marginalia. Once again, we see dialogic commentary on the primary text, with at least one annotator, the poem’s purported author Diatomis, being a Woman. The handwriting of Diatomis’ counterpart is strikingly similar to the handwriting of one of the annotators of the copy of Tetragonos’ memoirs discussed above, suggesting that Diatomis likely moved in the same social strata as Women such as Arcana and Synchordia. History records two Women named Diatomis who fit this description and were alive during the relevant time period: one was the sister of a Councilmember; the other was the granddaughter of a Councilmember Emeritus. The latter is known to have published more serious poetry, primarily a collection of naturalistic idyls, under a male pseudonym._

_A second woman is referenced: Favilla, apparently an employee of Diatomis, most likely a maid of some sort. That Favilla was apparently able to approach a publishing house, albeit one that was certainly not endorsed or subsidised by the Council, and present for publication a lurid, anonymously written poem, illustrates the relative freedom Women of the lower class had in some respects compared to their aristocratic counterparts. It was a freedom of anonymity; but with this dubious freedom came significant subjugation and disadvantage in terms of access to education, economic empowerment, and political power._

_The poem itself, for all that its tone and subject matter place it firmly in the territory of the lurid, with its vulgar punchline alluding to the Woman’s length and its depiction of Circles in concentric formation as if cannibalized or consumed in carnal deviance, nonetheless suggests that the anonymous poet may have been familiar with the Gospel of Three Dimensions. The ever-shrinking circumferences of the successive Priests evokes the accounts of those who have claimed over the years to have encountered a so-called three-dimensional “Sphere”: all of these accounts describe a Circle who could expand to formidable stature and then contract continuously until he was no more than a Point._

* * *

Lateralis leans forward to poke Diatomis in the side with her front end. “Pay attention,” she hisses.

Diatomis looks up, feigning innocence. She’s been scribbling furiously back and forth with Arcana in the margins of a large broadside, her maid, Favilla, following the movements of the stylus with interest. Whatever Arcana last wrote made both Diatomis and Favilla give her wide-eyed looks of mock outrage; they must be writing in feelprint, then, for Favilla is not yet fluent in reading lineprint although Diatomis has started teaching her the rudiments of it. 

In fact, since Favilla and her friend Kyma have joined them, the group of Women have taken to writing most of their notes in feelprint, so that they can all read each other’s records of the meetings. At Lateralis’ suggestion, they’ve also begun encrypting their notes. She came up with the idea four meetings ago, though the others at first thought she had gone insane when she showed them the meeting minutes in cipher. But, ‘We’re organised enough that it made sense to start keeping notes,’ she pointed out; and it’s true, now that they are a large enough group that not everyone can make every meeting, and have a voting system for collective decision-making, and have started tracking which Councilmembers might be influenced in favour of certain policies they have planted in their male relatives’ minds. ‘But do any of you want to risk the consequences if our notes are found?’

‘Are you suggesting that we can’t trust each other to keep such things properly hidden?’ Synechis was appalled. 

Arcana jumped at once to Lateralis’ defence. ‘I trust all of you,’ she said firmly. ‘But Lateralis is right; it cannot hurt to be careful.’

Lateralis gave her a grateful look. ‘It isn’t even that complicated a cipher,’ she added. ‘I can teach it to you in ten minutes. But it ought to at least throw off any prying fathers or husbands who come across anything written in here.’

Now, Lateralis is pleased to see that even though Arcana and Diatomis are passing notes during a meeting like wayward schoolchildren, they are at least doing so in cipher. Then she notices what they’re writing the notes _on_. 

“You got that _published_?” she squawks, forgetting to keep her own voice down.

Across the room, Synechis shoots the four of them — Lateralis, Diatomis, Favilla, and Arcana — a look of disapproval. Lateralis feels slightly guilty. Synechis still hasn’t warmed to Favilla, having opposed inviting her or indeed any Women from any class below Hexagons, to join them. Diatomis out-argued her on the issue — ‘We cannot claim to be working for the liberation of Women if we are not working for the liberation of _all_ Women,’ she’d said, surprising the others with her fervour — and Synechis was outvoted, but Lateralis thinks she still isn’t fully resigned to the expansion of their... what even are they, now? A club? An association? A cabal?

 _A movement,_ Lateralis thinks. _We’re a movement._

There’s sudden strength in that thought, and she moves back a bit and composes herself, looking steadily back at Synechis. Nevertheless, a part of her is still busy being aghast at the sight of Diatomis’ lurid verse, humourous enough when Favilla and Diatomis were reading it aloud to a small group of Women, printed on broadsides for public consumption. It is exactly, she thinks, the sort of risk they cannot afford to take, and leaning forward to read the feelprint notes again, she’s pleased to see that Arcana at least seems to agree.

Diatomis, though, is looking rather pleased with herself about the whole thing. “It was far too entertaining to be kept within our own confidence. Fear not, I made sure it cannot be traced to me, or to any of us.”

“Whoever you spoke to at the printing house might beg to differ,” Arcana mutters darkly.

“I spoke to no one at the printing house,” Diatomis retorts loftily. She and Favilla share a mischievous smile.

“I did,” Favilla explains. “They didn’t know who I work for, or even that I could read what I told them my employer had asked me to submit.”

Synechis glares. “It was still a terrible risk! And for quite a crude bit of verse.” It’s unclear which of those she sees as the greater outrage.

Diatomis seems rather proud of both accusations. “You wouldn’t believe how long it took me to find a rhyme for ‘viscera’,” she says blithely, “it seemed a shame not to share it once I finally did.”

Arcana is eyeing Diatomis and Favilla. “Perhaps we will escape detection this time. And honestly I do think it’s time we started planning for how to win over more of the citizenry; it’s all well and good to nudge the Men in our households toward one minor reform or another within the Council, but we’ll only have real leverage if they’re facing widespread public outcry.”

It’s a good point, Lateralis realizes. Arcana, as usual, is thinking two steps ahead. “We need to be united on what we’re presenting to the public, though,” she muses. “We ought to determine a procedure for approving proposed materials for publication.”

Diatomis groans. “We’ll be as mired in bureaucracy as the Council if we continue like this, Lateralis! Soon enough you’ll have us drafting procedures to govern the process of drafting procedures, and it will never end!”

“Process is important!” Lateralis fires back.

Rather to her surprise, Favilla comes to her aid. “We’re going to disagree about decisions, for certain. So we need to make sure we all agree that the way we arrive at our decisions is fair, and takes account of everyone’s thoughts, even if some of us—” she give Synechis a long look— “don’t like the result.”

Lateralis gives Favilla an approving look, and even Diatomis, despite her disgruntlement about the substance of the argument, seems rather proud. Favilla wouldn’t have challenged her publicly like that even two months ago; she’s grown. They all have. 

Arcana is smiling at Lateralis, encouraging beneath her amusement, and Lateralis thinks that perhaps one of the best results of their work over the last few years has been earning not merely her friend’s affection, but her respect. 

“Would anyone like to make a motion on the topic, then?” Arcana says, and Lateralis bites back a grin.

**Notes for the Chapter:**

> This chapter is entirely the fault of excellent human [jabez_dawes](https://archiveofourown.org/users/polly_oliver/pseuds/jabez_dawes).


	7. Minutes

Archival Document #588B-18

Description: Excerpt of minutes from a meeting of the Coalition for Linear Liberation with marginal note  
Date: Spring 2094

_[handwritten feelprint, encrypted]_

> Coalition for Linear Liberation
> 
> March 2094 meeting  
>  Quorum: Present  
>  Rotating chair: Arcana  
>  Minutes taker: Coalition Secretary
> 
> Agenda Item #1: Upcoming Council Vote on Granting Women Access to Public Sessions  
>  – Synechis gave summary of progress to date on persuading Councilmembers to vote in favour.  
>  – Current unofficial vote count: 42 in favour, 73 against, 12 undecided leaning yes, 9 undecided leaning no, 21 undecided (no indication).  
>  – Tasks to be completed: (1) Arcana to host supper party for 20 undecideds (including 7 currently leaning yes) to obtain updated vote count and try to swing votes; (2) Kyma to confirm delegation of Equilaterals to speak in favour; (3) Synchordia and Ephtheia to coordinate travel for Women seeking to attend vote. 
> 
> Agenda Item #2: Proposal to Open Coalition Meetings to Isosceles, Equilaterals, and Irregulars  
>  – Diatomis presented arguments in favour of proposal, including alignment of interests given existing concentration of power among Polygons and Circles, greater impact of public demonstrations, and deepening of movement resources.  
>  – Synechis presented arguments against proposal, including difficulty of coordinating greater numbers, divergence of interests in certain specific issue areas, and risk of discomfort to existing Coalition members.  
>  – Ephtheia offered compromise proposal to restrict admission of Men to Equilaterals; members present debated this proposal at length but reached no consensus.  
>  – Kyma offered compromise proposal to open every other meeting to Men designated in original proposal and maintain Women-only policy for remainder of meetings.  
>  – Vote delayed for consideration of alternate proposals.  
>  – Tasks to be completed: (1) Ephtheia to draft formal alternate proposal; (2) Kyma to draft formal alternate proposal.
> 
> Agenda Item #3: Approval of Anonymous Letter to the Editor on Women’s Access to Public Rights of Way  
>  – Letter reviewed.  
>  – Proposed amendments 1, 2, 6, 8, 9, and 10 approved.  
>  – Proposed amendments 3, 4, 5, and 7 rejected.  
>  – Vote held: 12 in favour of approving letter; 5 opposed; 2 abstaining. Letter approved for submission.
> 
> _[handwritten lineprint, encrypted]_
> 
> I stand beside her, parallel,  
>  In sisterhood resolved,  
>  Yet stifle sighs, and sighing dwell  
>  On theorems unsolved;  
>  For if the world were Space, not Flat,  
>  I might not sigh in vain,  
>  For Lines in parallel have met  
>  Upon a curvèd plane.

* * *

**Lemma’s notes:**

_These minutes illustrate that, by the mid-2090s, the loose association of Women coordinating efforts for the advancement of Women’s social, political, and economic rights had grown into a systematic, structured Coalition, with regular meetings, ordered decision-making procedures, and a membership large and committed enough to both generate and survive significant disagreement over the Movement’s aims, strategies, and tactics._

_The reference in the minutes to the proposal to open the Coalition to Men belonging to certain marginalized classes is particularly striking, as it was less than a year following the recording of this meeting that the first large cross-issue demonstration was held before the Hall of Governance. That demonstration included not only Women but also Equilaterals and Isosceles challenging the sidedness-based social hierarchies, and Irregulars protesting the stigma and discrimination they faced under the doctrine of Regularity._

_Most puzzling, however, is the short verse squeezed into the margin of the minutes. Analysis of the handwriting suggests that the author of the verse is the same Woman who was recording the minutes, though she wrote the former in lineprint and the latter in feelprint; analysis of the ink suggests that the two were written more or less contemporaneously, perhaps even in the same meeting._

 _The verse reflects the writer’s familiarity with the Gospel of Three Dimensions, as it refers to “a curvèd plane” — a physical impossibility in Flatland but a commonplace phenomenon in Spaceland, according to the available accounts. The assertion that parallel lines may meet upon a curved plane_2 _(subtly reinforced by the use of a slant rhyme between the fifth and seventh lines, whereby poetic lines bend to meet one another as the poet wishes human Lines could) suggests that by this point the Women who subscribed to the Gospel of Three Dimensions had made significant advances in developing the mathematics of a hypothetical three-dimensional world; this is particularly striking given that such theoretical developments would have been anathema to the Mathematics Faculties of established Flatland universities at the time._

_While the identity of the secretary-come-poet is not known, other documents indicate that of the likely leaders of the Coalition, those most interested in the mathematics of three dimensions were Kyma, Lateralis, and Arcana. As the rotating chair of the recorded meeting, Arcana would not have had the task of taking minutes; the writer, therefore, was probably Kyma or Lateralis, though I have found no evidence pointing conclusively to one or the other of them._

_The short poem speaks of solidarity, yet also, metaphorically, of division or separation that might be overcome in a three-dimensional world. Two interpretations of the verse’s meaning suggest themselves. The first is that it is a reflection on the class divisions that persisted among the Women of the Coalition: united though they were in many of their goals and organising efforts, they were not immune to the animosity and resentment caused by unequal access to reading and writing materials, resources, and power that arose out of their varied classes. Women associated with the Isosceles and Equilateral classes, including Kyma, thus often faced compounded marginalisation, and sometimes struggled to convince their aristocratic comrades of the validity of their grievances. For a lower-class Woman to write such a verse in lineprint, traditionally the province of the upper classes, would therefore have sent a pointed message._

_The second possible interpretation is perhaps even more radical: that this verse expresses romantic attraction between two Women present in the Coalition, or at least unrequited attraction on the part of one. Although the imagery is unique in its espousal of the Gospel of Three Dimensions, in form and tone it greatly resembles other romantic poetry of the era. While this interpretation, like the first, is necessarily speculative, it suggests, if it is true, that Flatland’s current socio-political controversies over sexual freedoms may have had their roots much, much earlier than previously surmised._

* * *

Lateralis sighs; the Council vote is going to be an uphill battle. Still, Arcana has worked miracles over dinner parties before.

She grows even more exasperated when the discussion turns to Diatomis’ proposal to open their meetings to Men, or certain Men, at least: Kyma’s husband and Favilla’s brothers, specifically. This would perhaps not present such a problem if one of Favilla’s brothers weren’t Irregular. Only by a degree and a half, which Lateralis personally thinks is hardly enough to count, but by the Regularity Restrictions it is enough to classify him a Scalene. More than a few of the Women present are horrified at the thought of associating with a Scalene. 

Synechis, predictably, seems horrified at the thought of associating with Men in this context at all, which Lateralis finds rather ironic given that much of what they are trying to achieve involves obtaining an equal footing with Men in the arena of politics, and proving that the dimensional differences between Lines and Shapes do not in fact carry over into differences of ability or aptitude. 

She is dutifully recording the meeting minutes without paying much attention to the debate, since it’s abundantly clear they will not be holding a vote on this proposal today, when Arcana speaks up.

“I think perhaps the differences between Men and Women are even less pronounced than most of us might guess, if my own family history is to be believed.” That piques everyone’s interest; ideological and strategic differences aside, the Coalition members present are united in their eagerness to hear hitherto concealed gossip about one of the most prominent families in Flatland. “My grandmother told me that during the Colour Revolt, her great-uncle — or perhaps her great-aunt —”

“How could she possibly confuse the two?” Synchordia asks. It’s clear that her mother has not yet shared this particular piece of family gossip even with her daughter. Arcana silences Synchordia with look.

“That’s precisely the point. You all know that during the Colour Revolt the same two-colour painting scheme was proposed for Circles and Women, as both groups could not be said to have distinct, separate sides. Well, our ancestor was a Circle, physically, but once painted, retreated from the family and, if my grandmother is to be believed, lived as a Woman to all outward appearances until the end of the Revolt and the Colour Ban. There was apparently even an affair of some sort with another Circle...”

This pronouncement is met with silence, the tenor of which varies from listener to listener: some are mortified, others shocked, and quite a few disgusted. Lateralis, however, finds herself intrigued, and strangely exhilarated. She has imagined, more than once, what her life would have been like had she been born as someone other than a Line, but this is the first she has heard of someone actually shaping their life around such a vision. And if two Circles could engage in those sorts of relations, why not two Lines…?

Synechis’ voice brings her crashing back to the present. “But surely such an arrangement could not last,” she says, rather faintly. “Any Circle caught in such an arrangement would provoke such a scandal that his family would never recover.”

“If the Chromatic Seditionists had prevailed, who is to say?”

“It must still be short-lived, ill-fated from the outset; it goes against every natural order of the world!”

“There are plenty who would say exactly that about Women in government,” Arcana says quietly. “Is this so different?” Lateralis carefully does not look at her. 

“Anyway,” Arcana goes on, “my point is that perhaps it is not enough simply to ask for one particular privilege here, and one particular privilege there, and hope to change things piece by piece. Perhaps we should be reexamining the roots of how we are divided. And that goes not only for us, but for Irregulars and Triangles as well.”

There is another long silence. Then Synchordia speaks up. “I agree, Mother.”

Lateralis wants to say that she does too, but her voice seems to have fled.

_________________________________

2 _Spaceland readers will recognize this as a feature of the branch of Mathematics we know as non-Euclidean geometry._


	8. Coda

Much later, Arcana and Lateralis watch over Synchordia as she sleeps. Worry still creases the corners of Arcana’s eye; it took her and Callocyclus two full days after the mass arrests at the demonstration to extract their daughter from the jail, and while Synchordia at least seems to have escaped the worst of the violence, she is clearly still exhausted from her ordeal.

“It seems as though, for every step forward we take,” Arcana murmurs, “we are pushed two steps back.”

Lateralis shifts slightly closer to her, offering solidarity and comfort. “We knew this would be a long struggle.”

“I am beginning to think we will not live to see the end of it.”

Lateralis is silent for a few moments. Her own eye is beginning to dim, her voice to grow scratchy with age. But the meetings are still going on, with many chapters now in many cities, filled with many unexpected allies. Sometimes, she and Arcana and the others still get caught passing notes like schoolchildren when they attend. “Perhaps not,” she says at last, and nods toward Synchordia, “but she may.” 

Arcana turns to her with a rather watery smile, and, very gently, Lateralis brushes away the tear that is about to fall.

* * *

**Translators' Endnote**

_The documents and notes presented here represent the selected excerpts of her ongoing research that we received from Lemma. We anticipate receiving a finished manuscript in the near future, and look forward to working with Lemma to prepare it for publication should she remain unable to publish it in Flatland. Lemma has notified us that she welcomes any reader feedback pertaining to these preliminary documents, as it will help her develop her research further and ultimately improve the quality of her eventual dissertation. —Trs._


End file.
